#-------------------------------------#
# Model for the deterministic problem #
#-------------------------------------#

param T;                # number of periods (time horizon)
set TIME := 0..T;
set TIME1:= 0..T-1;
set TIME2:= 1..T;
set TIME3:= {T};
set TIME4:= {0};
param x0        >= 0;   # initial state
param xTobj     >= 0;   # objective for the state
param b {TIME1} >= 0;   # bound for the control at each period
param xi{TIME2} ;       # perturbation
var x {TIME}    >= 0;   # state of the system at each period
var u {TIME}    >= 0;   # control for each period

# Objective function
minimize slack: sum{t in TIME3} (xTobj-x[t]);
# System dynamics
subject to timedynamics {t in TIME2}: x[t] = x[t-1] + u[t-1] - xi[t];
# Bound for the control variable
subject to timebound {t in TIME1}: u[t] <= b[t];
# Initial state of the system
subject to initial {t in TIME4} : x[t] = x0;